Question

What are the domain and range of the function f(x)=√x?

1) Domain: (6, [infinity]), Range: (0, [infinity])
2) Domain: [6, [infinity]), Range: (-[infinity], [infinity])
3) Domain: [0, [infinity]), Range: (6, [infinity])
4) Domain: [0, [infinity]), Range: [6, [infinity])

Answer 1

The domain and range of the function f(x)=√x are both [0, ∞), as the square root is defined only for non-negative numbers and the resulting value is also non-negative.

Step-by-step explanation:

To determine the domain and range of the function f(x)=√x, we need to consider the characteristics of the square root function. Since the square root of a number is defined only for non-negative numbers, the domain of f(x) is all real numbers greater than or equal to zero. This is because taking the square root of a negative number is not a real operation. Thus, f(x) is defined for all x such that x ≥ 0. Therefore, the domain is [0, ∞).

As for the range of f(x), it includes all the values that f(x) can take. The smallest value of f(x) is when x is 0, which is the square root of 0, thus f(0) = 0. As x increases, the value of f(x) increases without bound. Hence, the range of f(x) is all real numbers greater than or equal to 0, which can be represented as [0, ∞).

Given these explanations, the correct answer to the question about the domain and range of f(x)=√x is option 4: Domain: [0, ∞), Range: [0, ∞).